Combine celery, carrot, green pepper and onion in a slow cooker. Add broth, beer, salt and pepper. Cover and cook on LOW 5 to 6 hours.
After 5 or 6 hours, remove vegetables with a slotted spoon and process in a blender or food processor in batches until pureed and return to cooker with broth. Turn control to HIGH. Dissolve cornstarch in water; stir into pureed mixture. Add cheese gradually, stirring until blended. Cover and cook on HIGH 15 to 20 minutes. Serve hot.